A new-generation video coding standard, named High Efficiency Video Coding (HEVC), has recently been developed by JCT-VC. This new standard provides a significant improvement in picture quality, especially for high-resolution videos. However, one the most important challenges in HEVC is time complexity. A quadtree-based structure is created for the encoding and decoding processes and the rate-distortion (RD) cost is calculated for all possible dimensions of coding units in the quadtree. This provides a high encoding quality, but also causes computational complexity. We focus on a reduction scheme of the computational complexity and propose a new approach that can terminate the quadtree-based structure early, based on the RD costs of the parent and current levels. Our proposed algorithm is compared with HEVC Test Model version 10.0 software and a previously proposed algorithm. Experimental results show that our algorithm provides a significant time reduction for encoding, with only a small loss in video quality.